Proportions, Percentages and Ratios | Data Analysis

Article shared by

After reading this article you will learn about Proportions, Percentages and Ratios.

Proportions:

The proportion of cases in any given category is defined as the number in the category divided by the total number of cases. In calculation of proportions, it is presumed that the method of classification has been such that categories are mutually exclusive and the category-set exhaustive. That is, any given individual has been placed in one and only one category.

To illustrate, let us take a nominal scale consisting of four categories with n1 n2, n3, and n4 cases, respectively. Let the total number of cases be N. Hence, proportion of individuals in the first, second, third and fourth categories are n1/N, n2/N, n3/N, and n4/N respectively. The following illustration will clarify the point.

The proportion of science students among males is 75/317 or 0.236; the comparable figure for females is 60/226 or 0.265. Other proportions can be computed in a similar fashion and results summarised in tabular form (Table 18.4).

ADVERTISEMENTS:

The value of a proportion cannot be greater than unity, i.e., 1. Thus, if we add the proportions of cases in all categories, the result is unity. This is an important property of proportions.

Percentage:

The words per cent mean per hundred. Hence, percentage can be obtained from proportions by simply multiplying them by 100. In other words, percentage is the rate per hundred.

ADVERTISEMENTS:

The figures in Table 18.4 may just as well be expressed in terms of percentages.

Conventionally, percentages are calculated up to the nearest decimal and adjustments are made in the last digits so that totals come to exactly 100.

Ratio:

The ratio of any number A to another number B is defined as the numerical quantity obtained by dividing A by B. Suppose that there are 800 male students and 300 female students in M.A. (economics) class. The ratio of male students to female students is 800/300.

ADVERTISEMENTS:

In calculating ratio the key term is the word ‘to.’ Whatever quantity precedes this word is placed in the numerator while the quantity following it is treated as the denominator.

In practice, a ratio is either reduced to its simplest form by cancelling common factors or is expressed in terms of a denominator of unity. Thus, the ratio of male students to female students in the above example will be written as 8:3 or 2.66 to 1.

Proportion and Percentage:

ADVERTISEMENTS:

For use of proportions and percentages, the following rules of thumb are important:

(i) Total number of cases should be always reported along with proportions or percentages.

(ii) Percentages must not be computed unless the number of cases on which the percentage is based is in the neighbourhood of 50 or more.

(iii) Percentages may be computed in either direction and careful attention should be given to each table to determine exactly how each percentage has been obtained.